Crop succession requirements in agricultural production planning

A method is proposed to write crop succession requirements as linear constraints in an LP-based model for agricultural production planning. Crop succession information is given in the form of a set of inadmissible successions of crops. The decision variables represent the areas where a certain admissible sequence of crops is cultivated. The number of decision variables may be reduced by forming suitable combinations of crop sequences. For this purpose, an algorithm is presented. Also, multi-year linear programming models for farm production planning containing crop succession constraints are considered. It is shown that, under some regularity conditions, a stationary cropping plan is an optimal solution of such a model. Finally, it is discussed how to determine, given a collection of inadmissible sequences, crop sequences which are inadmissible but do not contain inadmissible subsequences. The length of the longest of these sequences determines the length of the crop sequences taken into account in the model.